Rectangle Dimensions Reduce Ratio

Reduce the dimensions of the rectangle with dimensions of 21 cm and 3 dm in a ratio of 4:6. In what proportion will the areas of both rectangles be?

Final Answer:

c =  14 cm
d =  20 cm
r =  9:4

Step-by-step explanation:

$$\begin{gathered} a=21\text{cm} \\ b=3\text{dm}\to \text{cm}=3\cdot 10\text{cm}=30\text{cm} \\ k=4:6\doteq 0.6667=2:3 \\ c=a\cdot k=21\cdot 0.6667=14\text{cm} \end{gathered}$$

$d=b\cdot k=30\cdot 0.6667=20\text{cm}$

$$\begin{gathered} S_1=a\cdot b=21\cdot 30=630{\text{cm}}^2 \\ {S}_2=c\cdot d=14\cdot 20=280{\text{cm}}^2 \\ r=S_1/S_2=630/280=2.25=9:4 \end{gathered}$$

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